PET is an imaging technique that produces a three-dimensional image of functional processes in an object or a portion thereof. Typically, biologically active molecules carrying radioactive tracer molecules may be introduced into the object. The tracer may undergo positron emission decay and emit a positron. The positron may annihilate with an electron, generating a pair of annihilation photons (e.g., gamma photons) that move in approximately opposite directions. The annihilation photons may be absorbed by a plurality of crystal elements (e.g., arranged in the form of one or more rings) that create bursts of optical photons (e.g., visible light photons) that, in turn, may be detected by photodetectors. Then the three-dimensional image of the object may be generated based on coincident photon detections. Because pairs of detected annihilation photons may travel along nearly straight lines (referred to as lines of response (LOR)), the tracer location may be determined by identifying LORs.
In conventional systems, a PET scanner exhibits a progressive reduction in spatial resolution with increased distance away from the center of its field of view (FOV). This resolution loss is at least partly caused by an uncertainty in assigning an LOR to a detected coincident event. The uncertainty of LOR assignment may be relatively smaller for a pair of detector modules located near the scanner's central axis (i.e., an axis along an axial direction of the scanner passing through the center of the FOV) than that located far from the central axis. Also, the uncertainty of LOR assignment may be relatively smaller for a pair of detector modules located closer to each other along the axial direction of the scanner than a pair of detector modules located far away from each other. For example, as illustrated in FIG. 2a, a pair of detector modules 201 and 202 is located nearer to the scanner's center axis than a pair of detector modules 203 and 204. As illustrated in FIG. 2b, the distance between the detector modules 201 and 202 along the axial direction of the scanner is smaller than that between a pair of detector modules 202 and 205. The dotted lines A and B define a range of possible LORs assigned to the detector modules 201 and 202, C and D define a range of possible LORs assigned to the detector modules 203 and 204, and E and F define a range of possible LORs assigned to the detector modules 202 and 205. The difference Δr1 between A and B is smaller than the difference Δr2 between C and D, suggesting a relative smaller resolution loss in detector modules 201 and 202 than detector modules 203 and 204. Similarly, the difference Δr1 is smaller than the difference Δr3 between E and F, suggesting a relative smaller resolution loss in detector modules 201 and 202 than detector modules 202 and 205.
Thus, in order to improve imaging resolution, it is desirable to determine the position or depth of photon gamma interactions occurred within a PET detector. PET imaging systems that provide depth of interaction (DOI) information can assign LORs to coincident events more accurately, thereby resulting in a more uniform resolution throughout the FOV. A plurality of techniques for extracting DOI information from a PET detector has been proposed. A possible way is to optically couple photon-sensors to both ends of a crystal element of a PET detector. For example, as illustrated in FIG. 3a, a photon-sensor 301a and a photon-sensor 301b are optically coupled to two ends of a crystal element 302, respectively. The DOI information of a photon gamma interaction (e.g., a photon gamma interaction 1) within the crystal element 302 may be determined based on the ratio of output energies from the photon-sensors 301a and 301b. 
Another exemplary way employs a photon-sensor array coupled to a monolithic crystal. For example, as illustrated in FIG. 3b, a photon-sensor array 303 including a plurality of photon-sensors 301c is optically coupled to a crystal element 304. The DOI information of photon gamma interaction (e.g., a photon gamma interaction 2 or 3) may be determined based on a distribution of outputs of the photon-sensors 301c. For example, when a photon gamma interaction excites one or more photons that are detected by more photon-sensors 301c, it may occur at a position farther away from the photon-sensor array 303.
Yet another exemplary way is based on multilayer crystals optically coupled with a photon-sensor array, and to determine the DOI information based on the characteristics of signals detected by the photon-sensor array. For example, as shown in FIG. 3c, a PET detector includes a first crystal layer 305, a second crystal layer 306, and a photon-sensor array 307 optically coupled to the second crystal layer 306. The properties of the crystals in different layers may be different. The above mentioned techniques may be applied in DOI determination, however, most of them rely on additional detector electronics, thereby requiring considerably more complicated hardware and possibly introducing other issues. Therefore, it is desirable to provide devices, systems, and methods for determining DOI in PET systems efficiently and accurately.